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A210450
Numbers n such that 16n + 7 is in A192628.
0
0, 3, 4, 5, 6, 7, 11, 16, 17, 21, 23, 24, 27, 28, 32, 34, 35, 36, 38, 39, 40, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 56, 59, 60, 63, 65, 67, 68, 69, 70, 72, 73, 74, 76, 77, 79, 81, 82, 85, 86, 89, 93, 96, 97, 98, 100, 102, 103, 105, 106, 107, 109, 110
OFFSET
1,2
COMMENTS
Reduce the elements of A192718 (which are the elements of A192628 congruent to 7 (mod 16)) by subtracting 7 and dividing by 16. In "On the reciprocal of the binary generating function for the sum of divisors", this sequence is precisely the set T.
LINKS
J. N. Cooper, D. Eichhorn, and K. O'Bryant, Reciprocals of binary power series, arXiv:math/0506496 [math.NT], 2005.
J. N. Cooper, D. Eichhorn, and K. O'Bryant, Reciprocals of binary power series, International Journal of Number Theory, 2 no. 4 (2006), 499-522.
J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, Journal of Integer Sequences, Vol. 16 (2013), #13.1.8.
PROG
(Sage)
prec = 2^12
R = PowerSeriesRing(GF(2), 'q', default_prec = prec)
q = R.gen()
sigma = lambda x : 1 if x == 0 else sum(Integer(x).divisors())
SigmaSeries = sum([sigma(m)*q^m for m in range(prec)])
SigmaBarSeries = 1/SigmaSeries
SigmaBarList = SigmaBarSeries.exponents()
reduced = [(m-7)/16 for m in SigmaBarList if mod(m, 8) == 7]
print(reduced[:128])
CROSSREFS
Sequence in context: A137922 A176984 A099562 * A133896 A052002 A247636
KEYWORD
nonn
AUTHOR
STATUS
approved